1. Field of Invention
The present application is directed towards systems and method for simulating a droplet evaporating on a substrate.
2. Description of Related Art
Applying inkjet technology to the industrial printing process can greatly improve its efficiency. Inkjet technology can be used to save energy, material, money, and it can also help improve the environment. Inkjet technology may be used in the manufacture of liquid crystal displays (LCD), thin film transistors (TFT), organic light emitting diodes (OLED), solar cells, micro-circuits, and other planar, layered, or 3-D structures. In the inkjet printing process, small droplets of a solution containing a solute with the desired properties and a solvent to make the solution jettable are deposited onto the target area. After the droplets reach the targeted area, the solvent evaporates and only the solute is left to form a final print pattern. The final pattern of the deposited solute directly determines the quality of the desired product.
In order to improve the quality of the final product, it is desirable to understand how the final pattern is formed in a realistic environment, what are the major factors affecting the final pattern, and how to control the production parameters in order to achieve a final product with the desired quality. In the final stage of the ink drying process, the aspect ratio of length to height becomes quite large. This makes it difficult to use traditional direct simulation methods to simulate the entire process. Lubrication equations may be applied to describe such phenomenon; however they can be difficult to implement in such a manner that artifacts near the contact line are not introduced. Prior art numerical methods have been limited to simulating systems in which the evaporation rate vanishes at the contact line. Prior art methods can not handle lubrication equations in which the evaporation rate does not vanish at the contact line.
In prior art methods, numerical artifacts creep into the simulation when a non-vanishing evaporation rate is used. An example of this is illustrated in FIGS. 1A-D. The prior art methods may be used to describe a droplet with an initial height profile of h(r,t=0)=1−r2 as shown in FIG. 1A. If radial symmetry is assumed then simulation may be reduced to one dimension. The system variables are written in terms of the axial radius. The system variables may also be averaged over the height of the droplet. It is reasonable to assume that the initial solute concentration is uniform (C=0.01) and that the capillary number is constant Ca=0.001. In this prior art example we assume that the evaporation rate is uniform (J=0.5). A prior art method was used to simulate the evaporation of a droplet, at (t=0.1) the droplet has a new profile shown in FIG. 1A.
FIG. 1B is an illustration of the total velocity integrated along the z-axis of the droplet at t=0.1 produced using a prior art simulation method. FIG. 1B also shows an artifact 102 that is produced when the prior art simulation method is used with a uniform evaporation model, which is a small wiggle close to the contact point of the droplet. FIG. 1C is an illustration of the solute film height which is the product of the concentration and the height (Ch) of the droplet at t=0.1, using a prior art simulation method. The solute film height is a system variable of interest. Artifact 104 shown in FIG. 1C is a strong fluctuation close to the contact point of the droplet produced by the prior art simulation method.
What has not been developed is a system or method for modeling a droplet with a uniform evaporation rate that does not produce large artifacts. The present invention is directed towards providing such a method.